A028939 - OEIS

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A028939

a(n) = denominator of y-coordinate of (2n)*P where P is the generator for rational points on the curve y^2 + y = x^3 - x.

1, 1, 1, 125, 64, 24389, 2146689, 274625, 50202571769, 4302115807744, 1469451780501769, 13528653463047586625, 343216282443844010111, 63061816101171948456692661, 495133617181351428873673516736

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OFFSET

1,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..86

B. Mazur, Arithmetic on curves, Bull. Amer. Math. Soc. 14 (1986), 207-259; see p. 225.

FORMULA

P=(0, 0), 2P=(1, 0); if kP=(a, b) then (k+1)P = (a' = (b^2-a^3)/a^2, b' = -1 - b*a'/a).

a(n) = A028943(2n). - Seiichi Manyama, Nov 19 2016

EXAMPLE

8P = (21/25, -69/125).

CROSSREFS

Cf. A028936, A028937, A028938 (numerator), A028943.

Sequence in context: A077495 A030668 A030678 * A195420 A080538 A104233

Adjacent sequences: A028936 A028937 A028938 * A028940 A028941 A028942

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

STATUS

approved